\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  42.0 & +  7.00 x_{1} & +  2.00 x_{2} & +  2.00 x_{3} & -3.00 x_{4} & -1.00 x_{5} & -10.00 x_{6} & -5.00 x_{7} & -7.00 x_{8} & +  8.00 x_{9}\\
 x_{11}   &  -21.0 & +  8.00 x_{1} & +  5.00 x_{2} & +  8.00 x_{3} & -9.00 x_{4} & +  2.00 x_{5} & +  4.00 x_{6} & +  3.00 x_{7} &    &   \\
 x_{12}   &  33.0 & -10.00 x_{1} & +  1.00 x_{2} & +  8.00 x_{3} & -10.00 x_{4} & +  3.00 x_{5} &   & +  2.00 x_{7} & -2.00 x_{8} & +  8.00 x_{9}\\
 x_{13}   &  22.0 & +  2.00 x_{1} & +  4.00 x_{2} & -9.00 x_{3} & -8.00 x_{4} & +  8.00 x_{5} & -3.00 x_{6} & -1.00 x_{7} &    &   \\
 x_{14}   &  12.0 & -1.00 x_{1} & -1.00 x_{2} & -9.00 x_{3} & -5.00 x_{4} & +  9.00 x_{5} & +  7.00 x_{6} & -7.00 x_{7} & +  8.00 x_{8} & -2.00 x_{9}\\
 x_{15}   &  97.0 & -1.00 x_{1} & -5.00 x_{2} & -6.00 x_{3} & -8.00 x_{4} & -6.00 x_{5} & -6.00 x_{6} & -7.00 x_{7} & -4.00 x_{8} & +  7.00 x_{9}\\
 x_{16}   &  -13.0 & +  4.00 x_{1} & -1.00 x_{2} &   & + 10.00 x_{4} & -4.00 x_{5} & +  3.00 x_{6} & -4.00 x_{7} & -7.00 x_{8} & +  5.00 x_{9}\\
 x_{17}   &  15.0 & -5.00 x_{1} & -6.00 x_{2} & -10.00 x_{3} & +  4.00 x_{4} & +  7.00 x_{5} & +  3.00 x_{6} & -1.00 x_{7} & +  2.00 x_{8} & -1.00 x_{9}\\
\hline
z    &  0.0 & +  4.00 x_{1} & -3.00 x_{2} & -1.00 x_{3} & +  5.00 x_{4} & -3.00 x_{5} & +  2.00 x_{6} & +  1.00 x_{7} & -2.00 x_{8} & +  4.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,17$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -7.00 y_{10} & -8.00 y_{11} & + 10.00 y_{12} & -2.00 y_{13} & +  1.00 y_{14} & +  1.00 y_{15} & -4.00 y_{16} & +  5.00 y_{17}\\
 y_{2}   &  1.0 & -2.00 y_{10} & -5.00 y_{11} & -1.00 y_{12} & -4.00 y_{13} & +  1.00 y_{14} & +  5.00 y_{15} & +  1.00 y_{16} & +  6.00 y_{17}\\
 y_{3}   &  1.0 & -2.00 y_{10} & -8.00 y_{11} & -8.00 y_{12} & +  9.00 y_{13} & +  9.00 y_{14} & +  6.00 y_{15} &   & + 10.00 y_{17}\\
 y_{4}   &  1.0 & +  3.00 y_{10} & +  9.00 y_{11} & + 10.00 y_{12} & +  8.00 y_{13} & +  5.00 y_{14} & +  8.00 y_{15} & -10.00 y_{16} & -4.00 y_{17}\\
 y_{5}   &  1.0 & +  1.00 y_{10} & -2.00 y_{11} & -3.00 y_{12} & -8.00 y_{13} & -9.00 y_{14} & +  6.00 y_{15} & +  4.00 y_{16} & -7.00 y_{17}\\
 y_{6}   &  1.0 & + 10.00 y_{10} & -4.00 y_{11} &   & +  3.00 y_{13} & -7.00 y_{14} & +  6.00 y_{15} & -3.00 y_{16} & -3.00 y_{17}\\
 y_{7}   &  1.0 & +  5.00 y_{10} & -3.00 y_{11} & -2.00 y_{12} & +  1.00 y_{13} & +  7.00 y_{14} & +  7.00 y_{15} & +  4.00 y_{16} & +  1.00 y_{17}\\
 y_{8}   &  1.0 & +  7.00 y_{10} &   & +  2.00 y_{12} &   & -8.00 y_{14} & +  4.00 y_{15} & +  7.00 y_{16} & -2.00 y_{17}\\
 y_{9}   &  1.0 & -8.00 y_{10} &   & -8.00 y_{12} &   & +  2.00 y_{14} & -7.00 y_{15} & -5.00 y_{16} & +  1.00 y_{17}\\
\hline
z    &  -0 & -42.00 y_{10} & + 21.00 y_{11} & -33.00 y_{12} & -22.00 y_{13} & -12.00 y_{14} & -97.00 y_{15} & + 13.00 y_{16} & -15.00 y_{17}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 3 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{11}   &  0.051724137931 & -0.71 y_{10} & -0.09 y_{1} & +  0.52 y_{12} & -0.45 y_{13} & -0.09 y_{14} & -0.19 y_{15} & +  0.03 y_{4} & +  0.57 y_{17}\\
 y_{2}   &  0.887931034483 & +  1.20 y_{10} & +  0.35 y_{1} & -2.12 y_{12} & -1.36 y_{13} & +  1.85 y_{14} & +  6.58 y_{15} & -0.24 y_{4} & +  3.27 y_{17}\\
 y_{3}   &  0.586206896552 & +  3.66 y_{10} & +  0.69 y_{1} & -12.14 y_{12} & + 12.59 y_{13} & +  9.69 y_{14} & +  7.52 y_{15} & -0.28 y_{4} & +  5.45 y_{17}\\
 y_{16}   &  0.146551724138 & -0.34 y_{10} & -0.08 y_{1} & +  1.47 y_{12} & +  0.40 y_{13} & +  0.42 y_{14} & +  0.63 y_{15} & -0.07 y_{4} & +  0.11 y_{17}\\
 y_{5}   &  1.48275862069 & +  1.07 y_{10} & -0.14 y_{1} & +  1.83 y_{12} & -5.52 y_{13} & -7.14 y_{14} & +  8.90 y_{15} & -0.34 y_{4} & -7.69 y_{17}\\
 y_{6}   &  0.353448275862 & + 13.84 y_{10} & +  0.58 y_{1} & -6.47 y_{12} & +  3.60 y_{13} & -7.92 y_{14} & +  4.87 y_{15} & +  0.07 y_{4} & -5.61 y_{17}\\
 y_{7}   &  1.43103448276 & +  5.78 y_{10} & -0.05 y_{1} & +  2.31 y_{12} & +  3.93 y_{13} & +  8.95 y_{14} & + 10.09 y_{15} & -0.38 y_{4} & -0.26 y_{17}\\
 y_{8}   &  2.02586206897 & +  4.65 y_{10} & -0.54 y_{1} & + 12.26 y_{12} & +  2.78 y_{13} & -5.04 y_{14} & +  8.41 y_{15} & -0.48 y_{4} & -1.22 y_{17}\\
 y_{9}   &  0.26724137931 & -6.32 y_{10} & +  0.39 y_{1} & -15.33 y_{12} & -1.98 y_{13} & -0.11 y_{14} & -10.15 y_{15} & +  0.34 y_{4} & +  0.44 y_{17}\\
\hline
z    &  2.99137931034 & -61.22 y_{10} & -2.82 y_{1} & -3.09 y_{12} & -26.26 y_{13} & -8.32 y_{14} & -92.80 y_{15} & -0.17 y_{4} & -1.59 y_{17}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  61.2155172414 & +  0.71 x_{11} & -1.20 x_{2} & -3.66 x_{3} & +  0.34 x_{16} & -1.07 x_{5} & -13.84 x_{6} & -5.78 x_{7} & -4.65 x_{8} & +  6.32 x_{9}\\
 x_{1}   &  2.81896551724 & +  0.09 x_{11} & -0.35 x_{2} & -0.69 x_{3} & +  0.08 x_{16} & +  0.14 x_{5} & -0.58 x_{6} & +  0.05 x_{7} & +  0.54 x_{8} & -0.39 x_{9}\\
 x_{12}   &  3.08620689655 & -0.52 x_{11} & +  2.12 x_{2} & + 12.14 x_{3} & -1.47 x_{16} & -1.83 x_{5} & +  6.47 x_{6} & -2.31 x_{7} & -12.26 x_{8} & + 15.33 x_{9}\\
 x_{13}   &  26.2586206897 & +  0.45 x_{11} & +  1.36 x_{2} & -12.59 x_{3} & -0.40 x_{16} & +  5.52 x_{5} & -3.60 x_{6} & -3.93 x_{7} & -2.78 x_{8} & +  1.98 x_{9}\\
 x_{14}   &  8.31896551724 & +  0.09 x_{11} & -1.85 x_{2} & -9.69 x_{3} & -0.42 x_{16} & +  7.14 x_{5} & +  7.92 x_{6} & -8.95 x_{7} & +  5.04 x_{8} & +  0.11 x_{9}\\
 x_{15}   &  92.8017241379 & +  0.19 x_{11} & -6.58 x_{2} & -7.52 x_{3} & -0.63 x_{16} & -8.90 x_{5} & -4.87 x_{6} & -10.09 x_{7} & -8.41 x_{8} & + 10.15 x_{9}\\
 x_{4}   &  0.172413793103 & -0.03 x_{11} & +  0.24 x_{2} & +  0.28 x_{3} & +  0.07 x_{16} & +  0.34 x_{5} & -0.07 x_{6} & +  0.38 x_{7} & +  0.48 x_{8} & -0.34 x_{9}\\
 x_{17}   &  1.59482758621 & -0.57 x_{11} & -3.27 x_{2} & -5.45 x_{3} & -0.11 x_{16} & +  7.69 x_{5} & +  5.61 x_{6} & +  0.26 x_{7} & +  1.22 x_{8} & -0.44 x_{9}\\
\hline
z    &  -2.99137931034 & -0.05 x_{11} & -0.89 x_{2} & -0.59 x_{3} & -0.15 x_{16} & -1.48 x_{5} & -0.35 x_{6} & -1.43 x_{7} & -2.03 x_{8} & -0.27 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  61.2155172414 & +  0.71 x_{11} & -1.20 x_{2} & -3.66 x_{3} & +  0.34 x_{16} & -1.07 x_{5} & -13.84 x_{6} & -5.78 x_{7} & -4.65 x_{8} & +  6.32 x_{9}\\
 x_{1}   &  2.81896551724 & +  0.09 x_{11} & -0.35 x_{2} & -0.69 x_{3} & +  0.08 x_{16} & +  0.14 x_{5} & -0.58 x_{6} & +  0.05 x_{7} & +  0.54 x_{8} & -0.39 x_{9}\\
 x_{12}   &  3.08620689655 & -0.52 x_{11} & +  2.12 x_{2} & + 12.14 x_{3} & -1.47 x_{16} & -1.83 x_{5} & +  6.47 x_{6} & -2.31 x_{7} & -12.26 x_{8} & + 15.33 x_{9}\\
 x_{13}   &  26.2586206897 & +  0.45 x_{11} & +  1.36 x_{2} & -12.59 x_{3} & -0.40 x_{16} & +  5.52 x_{5} & -3.60 x_{6} & -3.93 x_{7} & -2.78 x_{8} & +  1.98 x_{9}\\
 x_{14}   &  8.31896551724 & +  0.09 x_{11} & -1.85 x_{2} & -9.69 x_{3} & -0.42 x_{16} & +  7.14 x_{5} & +  7.92 x_{6} & -8.95 x_{7} & +  5.04 x_{8} & +  0.11 x_{9}\\
 x_{15}   &  92.8017241379 & +  0.19 x_{11} & -6.58 x_{2} & -7.52 x_{3} & -0.63 x_{16} & -8.90 x_{5} & -4.87 x_{6} & -10.09 x_{7} & -8.41 x_{8} & + 10.15 x_{9}\\
 x_{4}   &  0.172413793103 & -0.03 x_{11} & +  0.24 x_{2} & +  0.28 x_{3} & +  0.07 x_{16} & +  0.34 x_{5} & -0.07 x_{6} & +  0.38 x_{7} & +  0.48 x_{8} & -0.34 x_{9}\\
 x_{17}   &  1.59482758621 & -0.57 x_{11} & -3.27 x_{2} & -5.45 x_{3} & -0.11 x_{16} & +  7.69 x_{5} & +  5.61 x_{6} & +  0.26 x_{7} & +  1.22 x_{8} & -0.44 x_{9}\\
\hline
z    &  12.1379310345 & +  0.17 x_{11} & -3.21 x_{2} & -2.38 x_{3} & +  0.66 x_{16} & -0.72 x_{5} & -0.66 x_{6} & +  3.10 x_{7} & +  2.59 x_{8} & +  0.72 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  61.2155172414 & +  0.71 x_{11} & -1.20 x_{2} & -3.66 x_{3} & +  0.34 x_{16} & -1.07 x_{5} & -13.84 x_{6} & -5.78 x_{7} & -4.65 x_{8} & +  6.32 x_{9}\\
 x_{1}   &  2.81896551724 & +  0.09 x_{11} & -0.35 x_{2} & -0.69 x_{3} & +  0.08 x_{16} & +  0.14 x_{5} & -0.58 x_{6} & +  0.05 x_{7} & +  0.54 x_{8} & -0.39 x_{9}\\
 x_{12}   &  3.08620689655 & -0.52 x_{11} & +  2.12 x_{2} & + 12.14 x_{3} & -1.47 x_{16} & -1.83 x_{5} & +  6.47 x_{6} & -2.31 x_{7} & -12.26 x_{8} & + 15.33 x_{9}\\
 x_{13}   &  26.2586206897 & +  0.45 x_{11} & +  1.36 x_{2} & -12.59 x_{3} & -0.40 x_{16} & +  5.52 x_{5} & -3.60 x_{6} & -3.93 x_{7} & -2.78 x_{8} & +  1.98 x_{9}\\
 x_{14}   &  8.31896551724 & +  0.09 x_{11} & -1.85 x_{2} & -9.69 x_{3} & -0.42 x_{16} & +  7.14 x_{5} & +  7.92 x_{6} & -8.95 x_{7} & +  5.04 x_{8} & +  0.11 x_{9}\\
 x_{15}   &  92.8017241379 & +  0.19 x_{11} & -6.58 x_{2} & -7.52 x_{3} & -0.63 x_{16} & -8.90 x_{5} & -4.87 x_{6} & -10.09 x_{7} & -8.41 x_{8} & + 10.15 x_{9}\\
 x_{4}   &  0.172413793103 & -0.03 x_{11} & +  0.24 x_{2} & +  0.28 x_{3} & +  0.07 x_{16} & +  0.34 x_{5} & -0.07 x_{6} & +  0.38 x_{7} & +  0.48 x_{8} & -0.34 x_{9}\\
 x_{17}   &  1.59482758621 & -0.57 x_{11} & -3.27 x_{2} & -5.45 x_{3} & -0.11 x_{16} & +  7.69 x_{5} & +  5.61 x_{6} & +  0.26 x_{7} & +  1.22 x_{8} & -0.44 x_{9}\\
\hline
z    &  12.1379310345 & +  0.17 x_{11} & -3.21 x_{2} & -2.38 x_{3} & +  0.66 x_{16} & -0.72 x_{5} & -0.66 x_{6} & +  3.10 x_{7} & +  2.59 x_{8} & +  0.72 x_{9}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  55.8458574181 & +  0.65 x_{11} & -0.00 x_{2} & +  2.60 x_{3} & +  0.61 x_{16} & -5.68 x_{5} & -18.95 x_{6} & +  0.65 x_{14} & -7.90 x_{8} & +  6.25 x_{9}\\
 x_{1}   &  2.86705202312 & +  0.09 x_{11} & -0.36 x_{2} & -0.75 x_{3} & +  0.08 x_{16} & +  0.18 x_{5} & -0.53 x_{6} & -0.01 x_{14} & +  0.57 x_{8} & -0.39 x_{9}\\
 x_{12}   &  0.938342967245 & -0.54 x_{11} & +  2.60 x_{2} & + 14.64 x_{3} & -1.36 x_{16} & -3.67 x_{5} & +  4.42 x_{6} & +  0.26 x_{14} & -13.56 x_{8} & + 15.30 x_{9}\\
 x_{13}   &  22.6040462428 & +  0.41 x_{11} & +  2.18 x_{2} & -8.33 x_{3} & -0.21 x_{16} & +  2.38 x_{5} & -7.08 x_{6} & +  0.44 x_{14} & -4.99 x_{8} & +  1.93 x_{9}\\
 x_{7}   &  0.929672447013 & +  0.01 x_{11} & -0.21 x_{2} & -1.08 x_{3} & -0.05 x_{16} & +  0.80 x_{5} & +  0.89 x_{6} & -0.11 x_{14} & +  0.56 x_{8} & +  0.01 x_{9}\\
 x_{15}   &  83.4248554913 & +  0.09 x_{11} & -4.49 x_{2} & +  3.40 x_{3} & -0.15 x_{16} & -16.94 x_{5} & -13.80 x_{6} & +  1.13 x_{14} & -14.09 x_{8} & + 10.02 x_{9}\\
 x_{4}   &  0.525048169557 & -0.03 x_{11} & +  0.16 x_{2} & -0.13 x_{3} & +  0.05 x_{16} & +  0.65 x_{5} & +  0.27 x_{6} & -0.04 x_{14} & +  0.70 x_{8} & -0.34 x_{9}\\
 x_{17}   &  1.83526011561 & -0.57 x_{11} & -3.32 x_{2} & -5.73 x_{3} & -0.12 x_{16} & +  7.90 x_{5} & +  5.84 x_{6} & -0.03 x_{14} & +  1.36 x_{8} & -0.44 x_{9}\\
\hline
z    &  15.0231213873 & +  0.20 x_{11} & -3.85 x_{2} & -5.74 x_{3} & +  0.51 x_{16} & +  1.75 x_{5} & +  2.09 x_{6} & -0.35 x_{14} & +  4.34 x_{8} & +  0.76 x_{9}\\
\end{array}\]


 $ x_{5} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  54.3947506562 & +  1.49 x_{11} & -4.02 x_{2} & -20.04 x_{3} & +  2.71 x_{16} & +  1.55 x_{12} & -25.79 x_{6} & +  0.25 x_{14} & + 13.07 x_{8} & -17.41 x_{9}\\
 x_{1}   &  2.91286089239 & +  0.06 x_{11} & -0.24 x_{2} & -0.03 x_{3} & +  0.01 x_{16} & -0.05 x_{12} & -0.32 x_{6} & +  0.01 x_{14} & -0.09 x_{8} & +  0.36 x_{9}\\
 x_{5}   &  0.255643044619 & -0.15 x_{11} & +  0.71 x_{2} & +  3.99 x_{3} & -0.37 x_{16} & -0.27 x_{12} & +  1.20 x_{6} & +  0.07 x_{14} & -3.69 x_{8} & +  4.17 x_{9}\\
 x_{13}   &  23.2128608924 & +  0.06 x_{11} & +  3.86 x_{2} & +  1.17 x_{3} & -1.09 x_{16} & -0.65 x_{12} & -4.22 x_{6} & +  0.61 x_{14} & -13.79 x_{8} & + 11.86 x_{9}\\
 x_{7}   &  1.13359580052 & -0.11 x_{11} & +  0.36 x_{2} & +  2.10 x_{3} & -0.34 x_{16} & -0.22 x_{12} & +  1.85 x_{6} & -0.06 x_{14} & -2.38 x_{8} & +  3.34 x_{9}\\
 x_{15}   &  79.0937007874 & +  2.58 x_{11} & -16.49 x_{2} & -64.17 x_{3} & +  6.11 x_{16} & +  4.62 x_{12} & -34.20 x_{6} & -0.06 x_{14} & + 48.50 x_{8} & -60.59 x_{9}\\
 x_{4}   &  0.690551181102 & -0.13 x_{11} & +  0.62 x_{2} & +  2.45 x_{3} & -0.19 x_{16} & -0.18 x_{12} & +  1.05 x_{6} & +  0.00 x_{14} & -1.70 x_{8} & +  2.36 x_{9}\\
 x_{17}   &  3.85380577428 & -1.73 x_{11} & +  2.27 x_{2} & + 25.76 x_{3} & -3.04 x_{16} & -2.15 x_{12} & + 15.35 x_{6} & +  0.53 x_{14} & -27.81 x_{8} & + 32.47 x_{9}\\
\hline
z    &  15.4708661417 & -0.06 x_{11} & -2.61 x_{2} & +  1.25 x_{3} & -0.14 x_{16} & -0.48 x_{12} & +  4.20 x_{6} & -0.22 x_{14} & -2.14 x_{8} & +  8.06 x_{9}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{15} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  29.6930530673 & +  0.68 x_{11} & +  1.13 x_{2} & +  0.31 x_{15} & +  0.80 x_{16} & +  0.10 x_{12} & -15.10 x_{6} & +  0.27 x_{14} & -2.08 x_{8} & +  1.51 x_{9}\\
 x_{1}   &  2.87468607096 & +  0.06 x_{11} & -0.23 x_{2} & +  0.00 x_{15} & +  0.01 x_{16} & -0.05 x_{12} & -0.30 x_{6} & +  0.01 x_{14} & -0.11 x_{8} & +  0.39 x_{9}\\
 x_{5}   &  5.17178360779 & +  0.01 x_{11} & -0.32 x_{2} & -0.06 x_{15} & +  0.01 x_{16} & +  0.01 x_{12} & -0.92 x_{6} & +  0.07 x_{14} & -0.68 x_{8} & +  0.40 x_{9}\\
 x_{13}   &  24.6537986437 & +  0.11 x_{11} & +  3.56 x_{2} & -0.02 x_{15} & -0.98 x_{16} & -0.56 x_{12} & -4.84 x_{6} & +  0.61 x_{14} & -12.91 x_{8} & + 10.76 x_{9}\\
 x_{7}   &  3.72042522558 & -0.02 x_{11} & -0.18 x_{2} & -0.03 x_{15} & -0.14 x_{16} & -0.07 x_{12} & +  0.73 x_{6} & -0.06 x_{14} & -0.80 x_{8} & +  1.36 x_{9}\\
 x_{3}   &  1.23259381059 & +  0.04 x_{11} & -0.26 x_{2} & -0.02 x_{15} & +  0.10 x_{16} & +  0.07 x_{12} & -0.53 x_{6} & -0.00 x_{14} & +  0.76 x_{8} & -0.94 x_{9}\\
 x_{4}   &  3.70700910496 & -0.03 x_{11} & -0.01 x_{2} & -0.04 x_{15} & +  0.04 x_{16} & -0.00 x_{12} & -0.26 x_{6} & +  0.00 x_{14} & +  0.15 x_{8} & +  0.05 x_{9}\\
 x_{17}   &  35.6107279882 & -0.69 x_{11} & -4.35 x_{2} & -0.40 x_{15} & -0.59 x_{16} & -0.30 x_{12} & +  1.62 x_{6} & +  0.50 x_{14} & -8.34 x_{8} & +  8.14 x_{9}\\
\hline
z    &  17.0062704003 & -0.00 x_{11} & -2.93 x_{2} & -0.02 x_{15} & -0.02 x_{16} & -0.39 x_{12} & +  3.54 x_{6} & -0.22 x_{14} & -1.19 x_{8} & +  6.89 x_{9}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  1.96596042578 & +  0.04 x_{11} & +  0.07 x_{2} & +  0.02 x_{15} & +  0.05 x_{16} & +  0.01 x_{12} & -0.07 x_{10} & +  0.02 x_{14} & -0.14 x_{8} & +  0.10 x_{9}\\
 x_{1}   &  2.28587576895 & +  0.05 x_{11} & -0.25 x_{2} & -0.01 x_{15} & -0.01 x_{16} & -0.05 x_{12} & +  0.02 x_{10} & +  0.00 x_{14} & -0.07 x_{8} & +  0.36 x_{9}\\
 x_{5}   &  3.35979856766 & -0.03 x_{11} & -0.39 x_{2} & -0.08 x_{15} & -0.04 x_{16} & +  0.01 x_{12} & +  0.06 x_{10} & +  0.05 x_{14} & -0.55 x_{8} & +  0.31 x_{9}\\
 x_{13}   &  15.1402941865 & -0.11 x_{11} & +  3.20 x_{2} & -0.12 x_{15} & -1.24 x_{16} & -0.60 x_{12} & +  0.32 x_{10} & +  0.52 x_{14} & -12.24 x_{8} & + 10.27 x_{9}\\
 x_{7}   &  5.15029430841 & +  0.01 x_{11} & -0.13 x_{2} & -0.02 x_{15} & -0.10 x_{16} & -0.06 x_{12} & -0.05 x_{10} & -0.04 x_{14} & -0.90 x_{8} & +  1.43 x_{9}\\
 x_{3}   &  0.184720065104 & +  0.02 x_{11} & -0.30 x_{2} & -0.03 x_{15} & +  0.07 x_{16} & +  0.07 x_{12} & +  0.04 x_{10} & -0.01 x_{14} & +  0.83 x_{8} & -1.00 x_{9}\\
 x_{4}   &  3.19989871512 & -0.04 x_{11} & -0.03 x_{2} & -0.04 x_{15} & +  0.03 x_{16} & -0.00 x_{12} & +  0.02 x_{10} & -0.00 x_{14} & +  0.19 x_{8} & +  0.02 x_{9}\\
 x_{17}   &  38.7891923072 & -0.62 x_{11} & -4.23 x_{2} & -0.37 x_{15} & -0.50 x_{16} & -0.29 x_{12} & -0.11 x_{10} & +  0.53 x_{14} & -8.56 x_{8} & +  8.31 x_{9}\\
\hline
z    &  23.9610960433 & +  0.15 x_{11} & -2.67 x_{2} & +  0.05 x_{15} & +  0.17 x_{16} & -0.36 x_{12} & -0.23 x_{10} & -0.16 x_{14} & -1.68 x_{8} & +  7.24 x_{9}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  1.98449757176 & +  0.05 x_{11} & +  0.04 x_{2} & +  0.02 x_{15} & +  0.06 x_{16} & +  0.01 x_{12} & -0.06 x_{10} & +  0.02 x_{14} & -0.05 x_{8} & -0.10 x_{3}\\
 x_{1}   &  2.35231582282 & +  0.05 x_{11} & -0.36 x_{2} & -0.02 x_{15} & +  0.01 x_{16} & -0.03 x_{12} & +  0.03 x_{10} & -0.00 x_{14} & +  0.23 x_{8} & -0.36 x_{3}\\
 x_{5}   &  3.41708399623 & -0.02 x_{11} & -0.48 x_{2} & -0.09 x_{15} & -0.02 x_{16} & +  0.03 x_{12} & +  0.07 x_{10} & +  0.05 x_{14} & -0.30 x_{8} & -0.31 x_{3}\\
 x_{13}   &  17.0420243115 & +  0.06 x_{11} & +  0.15 x_{2} & -0.39 x_{15} & -0.55 x_{16} & +  0.10 x_{12} & +  0.68 x_{10} & +  0.41 x_{14} & -3.70 x_{8} & -10.30 x_{3}\\
 x_{7}   &  5.41474546674 & +  0.03 x_{11} & -0.55 x_{2} & -0.06 x_{15} & -0.01 x_{16} & +  0.04 x_{12} & +  0.00 x_{10} & -0.06 x_{14} & +  0.29 x_{8} & -1.43 x_{3}\\
 x_{9}   &  0.185152088566 & +  0.02 x_{11} & -0.30 x_{2} & -0.03 x_{15} & +  0.07 x_{16} & +  0.07 x_{12} & +  0.04 x_{10} & -0.01 x_{14} & +  0.83 x_{8} & -1.00 x_{3}\\
 x_{4}   &  3.20388014025 & -0.04 x_{11} & -0.03 x_{2} & -0.04 x_{15} & +  0.03 x_{16} & -0.00 x_{12} & +  0.02 x_{10} & -0.00 x_{14} & +  0.21 x_{8} & -0.02 x_{3}\\
 x_{17}   &  40.3271245805 & -0.48 x_{11} & -6.70 x_{2} & -0.59 x_{15} & +  0.05 x_{16} & +  0.28 x_{12} & +  0.19 x_{10} & +  0.44 x_{14} & -1.65 x_{8} & -8.33 x_{3}\\
\hline
z    &  25.3017609684 & +  0.27 x_{11} & -4.82 x_{2} & -0.14 x_{15} & +  0.65 x_{16} & +  0.13 x_{12} & +  0.02 x_{10} & -0.24 x_{14} & +  4.34 x_{8} & -7.26 x_{3}\\
\end{array}\]


 $ x_{8} $ enters and $ x_{13} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  1.73407647117 & +  0.05 x_{11} & +  0.04 x_{2} & +  0.02 x_{15} & +  0.07 x_{16} & +  0.01 x_{12} & -0.07 x_{10} & +  0.01 x_{14} & +  0.01 x_{13} & +  0.05 x_{3}\\
 x_{1}   &  3.39380011163 & +  0.06 x_{11} & -0.35 x_{2} & -0.04 x_{15} & -0.02 x_{16} & -0.02 x_{12} & +  0.07 x_{10} & +  0.02 x_{14} & -0.06 x_{13} & -0.99 x_{3}\\
 x_{5}   &  2.05613000753 & -0.03 x_{11} & -0.49 x_{2} & -0.06 x_{15} & +  0.03 x_{16} & +  0.02 x_{12} & +  0.02 x_{10} & +  0.01 x_{14} & +  0.08 x_{13} & +  0.51 x_{3}\\
 x_{8}   &  4.60216434877 & +  0.02 x_{11} & +  0.04 x_{2} & -0.11 x_{15} & -0.15 x_{16} & +  0.03 x_{12} & +  0.18 x_{10} & +  0.11 x_{14} & -0.27 x_{13} & -2.78 x_{3}\\
 x_{7}   &  6.7490291966 & +  0.04 x_{11} & -0.54 x_{2} & -0.09 x_{15} & -0.05 x_{16} & +  0.04 x_{12} & +  0.06 x_{10} & -0.03 x_{14} & -0.08 x_{13} & -2.24 x_{3}\\
 x_{9}   &  4.01032606122 & +  0.03 x_{11} & -0.26 x_{2} & -0.11 x_{15} & -0.06 x_{16} & +  0.09 x_{12} & +  0.19 x_{10} & +  0.08 x_{14} & -0.22 x_{13} & -3.31 x_{3}\\
 x_{4}   &  4.16067270918 & -0.04 x_{11} & -0.02 x_{2} & -0.07 x_{15} & +  0.00 x_{16} & +  0.01 x_{12} & +  0.06 x_{10} & +  0.02 x_{14} & -0.06 x_{13} & -0.60 x_{3}\\
 x_{17}   &  32.7138031845 & -0.51 x_{11} & -6.76 x_{2} & -0.41 x_{15} & +  0.30 x_{16} & +  0.23 x_{12} & -0.12 x_{10} & +  0.26 x_{14} & +  0.45 x_{13} & -3.73 x_{3}\\
\hline
z    &  45.2643316561 & +  0.34 x_{11} & -4.65 x_{2} & -0.60 x_{15} & +  0.01 x_{16} & +  0.25 x_{12} & +  0.82 x_{10} & +  0.25 x_{14} & -1.17 x_{13} & -19.32 x_{3}\\
\end{array}\]


 $ x_{10} $ enters and $ x_{6} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  23.8476731397 & +  0.63 x_{11} & +  0.59 x_{2} & +  0.33 x_{15} & +  0.93 x_{16} & +  0.17 x_{12} & -13.75 x_{6} & +  0.14 x_{14} & +  0.20 x_{13} & +  0.70 x_{3}\\
 x_{1}   &  5.16584253986 & +  0.10 x_{11} & -0.31 x_{2} & -0.01 x_{15} & +  0.05 x_{16} & -0.01 x_{12} & -1.02 x_{6} & +  0.03 x_{14} & -0.05 x_{13} & -0.94 x_{3}\\
 x_{5}   &  2.47030472026 & -0.02 x_{11} & -0.48 x_{2} & -0.05 x_{15} & +  0.04 x_{16} & +  0.02 x_{12} & -0.24 x_{6} & +  0.02 x_{14} & +  0.08 x_{13} & +  0.52 x_{3}\\
 x_{8}   &  9.00529759799 & +  0.13 x_{11} & +  0.15 x_{2} & -0.05 x_{15} & +  0.02 x_{16} & +  0.06 x_{12} & -2.54 x_{6} & +  0.14 x_{14} & -0.23 x_{13} & -2.65 x_{3}\\
 x_{7}   &  8.08206992426 & +  0.07 x_{11} & -0.51 x_{2} & -0.07 x_{15} & +  0.00 x_{16} & +  0.05 x_{12} & -0.77 x_{6} & -0.02 x_{14} & -0.07 x_{13} & -2.20 x_{3}\\
 x_{9}   &  8.51362909152 & +  0.15 x_{11} & -0.15 x_{2} & -0.05 x_{15} & +  0.12 x_{16} & +  0.12 x_{12} & -2.60 x_{6} & +  0.11 x_{14} & -0.19 x_{13} & -3.18 x_{3}\\
 x_{4}   &  5.50150661469 & -0.00 x_{11} & +  0.01 x_{2} & -0.05 x_{15} & +  0.05 x_{16} & +  0.01 x_{12} & -0.77 x_{6} & +  0.03 x_{14} & -0.04 x_{13} & -0.56 x_{3}\\
 x_{17}   &  29.8838429814 & -0.58 x_{11} & -6.83 x_{2} & -0.45 x_{15} & +  0.19 x_{16} & +  0.21 x_{12} & +  1.63 x_{6} & +  0.24 x_{14} & +  0.42 x_{13} & -3.81 x_{3}\\
\hline
z    &  64.8859801665 & +  0.86 x_{11} & -4.16 x_{2} & -0.33 x_{15} & +  0.78 x_{16} & +  0.39 x_{12} & -11.32 x_{6} & +  0.37 x_{14} & -1.01 x_{13} & -18.74 x_{3}\\
\end{array}\]


 $ x_{11} $ enters and $ x_{17} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  56.1405368993 & -1.08 x_{17} & -6.80 x_{2} & -0.16 x_{15} & +  1.13 x_{16} & +  0.40 x_{12} & -11.99 x_{6} & +  0.40 x_{14} & +  0.66 x_{13} & -3.42 x_{3}\\
 x_{1}   &  10.390484948 & -0.17 x_{17} & -1.50 x_{2} & -0.09 x_{15} & +  0.08 x_{16} & +  0.03 x_{12} & -0.74 x_{6} & +  0.08 x_{14} & +  0.03 x_{13} & -1.60 x_{3}\\
 x_{5}   &  1.62294792403 & +  0.03 x_{17} & -0.29 x_{2} & -0.04 x_{15} & +  0.04 x_{16} & +  0.02 x_{12} & -0.29 x_{6} & +  0.01 x_{14} & +  0.07 x_{13} & +  0.63 x_{3}\\
 x_{8}   &  15.7656771678 & -0.23 x_{17} & -1.40 x_{2} & -0.15 x_{15} & +  0.07 x_{16} & +  0.11 x_{12} & -2.17 x_{6} & +  0.19 x_{14} & -0.14 x_{13} & -3.51 x_{3}\\
 x_{7}   &  11.8059065154 & -0.12 x_{17} & -1.36 x_{2} & -0.12 x_{15} & +  0.02 x_{16} & +  0.08 x_{12} & -0.57 x_{6} & +  0.01 x_{14} & -0.01 x_{13} & -2.67 x_{3}\\
 x_{9}   &  16.1129819348 & -0.25 x_{17} & -1.89 x_{2} & -0.17 x_{15} & +  0.17 x_{16} & +  0.18 x_{12} & -2.18 x_{6} & +  0.17 x_{14} & -0.08 x_{13} & -4.15 x_{3}\\
 x_{4}   &  5.4948308466 & +  0.00 x_{17} & +  0.01 x_{2} & -0.05 x_{15} & +  0.05 x_{16} & +  0.01 x_{12} & -0.77 x_{6} & +  0.03 x_{14} & -0.04 x_{13} & -0.56 x_{3}\\
 x_{11}   &  51.3340173587 & -1.72 x_{17} & -11.74 x_{2} & -0.78 x_{15} & +  0.32 x_{16} & +  0.37 x_{12} & +  2.80 x_{6} & +  0.41 x_{14} & +  0.73 x_{13} & -6.54 x_{3}\\
\hline
z    &  108.893730172 & -1.47 x_{17} & -14.23 x_{2} & -1.00 x_{15} & +  1.05 x_{16} & +  0.71 x_{12} & -8.91 x_{6} & +  0.72 x_{14} & -0.38 x_{13} & -24.35 x_{3}\\
\end{array}\]


 $ x_{12} $ enters and Unbounded Dictionary!


 $ x_{12} $ enters and Unbounded Dictionary!
\end{document}
